WASHINGTON — Supreme Court justices appeared skeptical Wednesday of a city's decision to throw out the results of a firefighter promotion test after blacks scored disproportionately lower than whites. Yet it was unclear how much leeway the court might leave employers nationwide to make sure tests and other job criteria don't exclude minorities.

Many questions in the New Haven, Conn., case that could affect public and private employers came down to when managers can take account of race.

"How do you draw the line between race-conscious (action) that's permitted and racial discrimination that's not?" Chief Justice John Roberts asked. He and other conservative justices suggested New Haven had crossed the line.

Justice Anthony Kennedy, the swing vote on such disputes, indicated that the white firefighters who sued New Haven for invalidating results that could have earned them promotions might have a valid claim of intentional discrimination. The city "looked at the results," he said, "and it classified the successful and unsuccessful applicants by race."

Kennedy also raised concerns about how to assess employers' efforts to ensure that testing and other policies do not exclude minorities.

The case is one of several race-related dilemmas before the justices this term. Among the spectators was Eric Holder, the nation's first black attorney general, who earlier in the morning session was officially presented at the court.

New Haven officials canceled the results of a 2003 exam after no blacks and only two Hispanic applicants qualified for promotions based on their scores. (Of the 118 applicants who took the test, 50 were racial or ethnic minorities.) City officials said they feared claims of bias from the minorities. They said they also believed the test was flawed in determining the best promotion candidates.

Title VII of the 1964 Civil Rights Act bars direct discrimination based on race or sex. It also restricts indirect bias that might arise from tests or other standards that end up disproportionately disqualifying minorities or women from jobs.

Justice David Souter, among the liberal justices who seemed to support the city, said officials could have believed "there is such a racial disparity here that we are … walking blindly … into a racial disparity lawsuit."

Christopher Meade, representing New Haven officials, said employers should be able to "root out barriers to equal opportunity" by having the discretion to redo a test that may be biased.

"They get do-overs until it comes out right?" Roberts asked.

Meade said an employer should not be able to try tests over and over, yet it should at least be able to give a second test that it believes is a fairer, less discriminatory alternative.

"The question here is whether there is in fact a fair process," Meade said.

The Justice Department supports the city on that point. Deputy Solicitor General Edwin Kneedler said New Haven was trying to ensure that its test was not discriminatory. Once it saw the results, he said, "The employer paused and decided that there might be another … less discriminatory means."